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RegularChains[SemiAlgebraicSetTools]

  

RepresentingRootIndex

  

return the root index in a parametric box

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RepresentingRootIndex(pbx,R)

Parameters

pbx

-

parametric box

R

-

polynomial ring

Description

• 

The command RepresentingRootIndex(pbx,R) returns the representing root index in a parametric box.

  

See the page SemiAlgebraicSetTools for the definitions of a regular semi-algebraic set, a parametric box and a box.

Examples

withRegularChains:

withParametricSystemTools:

withSemiAlgebraicSetTools:

RPolynomialRingx,d,a,b,c

Rpolynomial_ring

(1)

Determine under which conditions on a,b,c,d the equation x2+d=0 has 2 distinct real solutions provided that d satisfies ad2+bd+c=0.

Fx2+d,ad2+bd+c

Fx2+d,ad2+bd+c

(2)

N

N

(3)

P

P

(4)

H

H

(5)

rrcRealRootClassificationF,N,P,H,4,2,R

rrcregular_semi_algebraic_set,border_polynomial

(6)

rsasrrc11

rsasregular_semi_algebraic_set

(7)

rbxRepresentingBoxrsas,R

rbxparametric_box

(8)

DisplayParametricBoxrbx:

d<0

AND

c1&colon;d2a+db+c&equals;0

(9)

RepresentingRootIndexrbx

1

(10)

See Also

IsParametricBox

RealRootClassification

RegularChains

RepresentingBox

RepresentingChain

RepresentingChain

RepresentingQuantifierFreeFormula

RepresentingRootIndex

VariableOrdering